Eigen-mode encoding of signals in a data group

1. A method of encoding N signals for transmission over a transmission line having N+1 conductors, wherein N is an integer greater than one and wherein the N signals include signals in(0) through in(N-1), the method comprising the steps of: determining electrical characteristics of the transmission line, wherein the step of determining includes the steps of: calculating an inductance matrix (L) for the conductors in the transmission line; calculating an electrostatic induction matrix (B) for the conductors in the transmission line; and calculating an eigen-mode encoding matrix (Sv) as a function of the inductance (L) and electrostatic induction (B) matrices; and encoding the N signals into N+1 encoded signals comprising signals enc(0) through enc(N), wherein the step of encoding comprises the step of encoding in(N-1) as a function of the eigen-mode encoding matrix (Sv).

2. The method according to claim 1, wherein the step of encoding in(N-1) as a function of the eigen-mode encoding matrix includes the step of multiplying an input signal vector D by the eigen-mode encoding matrix (Sv).

3. A method of encoding N signals for transmission over a plurality of different transmission lines, wherein each transmission line has N+1 conductors, wherein N is an integer greater than one and wherein the N signals include signals in(0) through in(N-1), the method comprising the steps of: determining electrical characteristics of each of the plurality of transmission lines, wherein the step of determining includes the steps of: calculating an inductance matrix (L) for the conductors in each transmission line; calculating an electrostatic induction matrix (B) for the conductors in each transmission line; calculating a generalized eigen-mode encoding matrix (Sv) as a function of each of the plurality of inductance (L) and electrostatic induction (B) matrices; and encoding the N signals into N+1 encoded signals comprising signals enc(0) through enc(N), wherein the step of encoding comprises the step of encoding in(N-1) as a function of the eigen-mode encoding matrix (Sv).

4. The method according to claim 3, wherein the step of encoding in(N-1) as a function of the eigen-mode encoding matrix includes the step of multiplying an input signal vector D by the eigen-mode encoding matrix (Sv).

5. A method of decoding N+1 eigen-mode encoded signals, wherein N is an integer greater than one, wherein the N+1 signals include signals enc(0) through enc(N) and wherein the eigen-mode encoded signals are encoded as a function of an eigen-mode encoding matrix (Sv), the method comprising the steps of: determining an eigen-mode decoding matrix (Sv_inv) as a function of the eigen-mode encoding matrix (Sv); decoding the N+1 eigen-mode encoded signals enc(0) through enc(N) into N output signals comprising signals out(0) through out(N-1), wherein the step of decoding comprises the step of decoding enc(N) as a function of the eigen-mode decoding matrix (Sv_inv).

6. The method according to claim 5, wherein the step of decoding enc(N) as a function of the eigen-mode decoding matrix includes the step of multiplying a vector including enc(N) by the eigen-mode decoding matrix (Sv_inv).

7. A communications system, comprising: a transmission line having N+1 conductors, wherein N is an integer greater than one; an eigen-mode encoder/driver connected to the transmission line, wherein the eigen-mode encoder/driver encodes input signals as a function of an eigen-mode encoding matrix (Sv), wherein the eigen-mode encoding matrix (Sv) is a function of an inductance matrix (L) and an electrostatic induction matrix (B) calculated for the conductors in the transmission line; and an eigen-mode receiver connected to the transmission line, wherein the eigen-mode receiver decodes signals received from the transmission line as a function of the eigen-mode encoding matrix (Sv).

8. The communications system according to claim 7, wherein the eigen-mode receiver decodes signals received from the transmission line as a function of an inverse of the eigen-mode encoding matrix (Sv).

9. A full duplex communications system, comprising: a transmission line having N+1 conductors, wherein N is an integer greater than one; a first and a second eigen-mode encoder/driver, wherein each encoder/driver is connected to the transmission line and wherein each eigen-mode encoder/driver encodes input signals as a function of an eigen-mode encoding matrix (Sv), wherein the eigen-mode encoding matrix (Sv) is a function of an inductance matrix (L) and an electrostatic induction matrix (B) calculated for the conductors in the transmission line; and a first and a second eigen-mode receiver, wherein each eigcn-mode receiver is connected to the transmission line and wherein each eigen-mode receiver decodes signals received from the transmission line as a function of the eigen-mode encoding matrix (Sv).

10. The full duplex communications system according to claim 9, wherein the eigen-mode receiver decodes signals received from the transmission line as a function of an inverse of the eigen-mode encoding matrix (Sv).

11. An eigen-mode encoder for driving an eigen-mode encoded signal over a transmission line having a plurality of conductors, the eigen-mode encoder comprising: N input lines, wherein N is greater than one; N+1 output lines; and an encoding circuit connected to the N input lines and the N+1 output lines, wherein the encoding circuit encodes signals received on the N input lines into N+1 eigen-mode encoded signals and drives the N+1 eigen-mode encode signals out onto the N+1 output lines, wherein the eigen-mode encoded signals are encoded as a function of an eigen-mode encoding matrix (Sv), wherein the eigen-mode encoding matrix (Sv) is a function of an inductance matrix (L) and an electrostatic induction matrix (B) calculated for conductors in the transmission line.

12. An eigen-mode decoder for receiving and decoding an eigen-mode encoded signal over a transmission line having a plurality of conductors, wherein the eigen-mode encoded signals are encoded as a function of an eigen-mode encoding matrix (Sv), the eigen-mode decoder comprising: N+1 input lines, wherein N is greater than one; N output lines; and a decoding circuit connected to the N+1 input lines and the N output lines, wherein the decoding circuit decodes signals received on the N+1 input lines into N output signals and drives the N output signals out onto the N output lines, wherein the input signals are decoded as a function of the eigen-mode encoding matrix (Sv).

13. The full duplex communications system according to claim 12, wherein the eigen-mode receiver decodes signals received from the transmission line as a function of an inverse of the eigen-mode encoding matrix (Sv).